Maximum Getis–Ord Statistic Adjusted for Spatially Autocorrelated Data

Local statistics test the null hypothesis of no spatial association or clustering around the vicinity of a location. To carry out statistical tests, it is assumed that the observations are independent and that they exhibit no global spatial autocorrelation. In this article, approaches to account for global spatial autocorrelation are described and illustrated for the case of the Getis–Ord statistic with binary weights. Although the majority of current applications of local statistics assume that the spatial scale of the local spatial association (as specified via weights) is known, it is more often the case that it is unknown. The approaches described here cover the cases of testing local statistics for the cases of both known and unknown weights, and they are based upon methods that have been used with aspatial data, where the objective is to find changepoints in temporal data. After a review of the Getis–Ord statistic, the article provides a review of its extension to the case where the objective is to choose the best set of binary weights to estimate the spatial scale of the local association and assess statistical significance. Modified approaches that account for spatially autocorrelated data are then introduced and discussed. Finally, the method is illustrated using data on leukemia in central New York, and some concluding comments are made.